Information compression is essential to reduce communication cost in distributed optimization over peer-to-peer networks. This paper proposes a communication-efficient linearly convergent distributed (COLD) algorithm to solve strongly convex optimization problems. By compressing innovation vectors, which are the differences between decision vectors and their estimates, COLD is able to achieve linear convergence for a class of δ-contracted compressors. We explicitly quantify how the compression affects the convergence rate and show that COLD matches the same rate of its uncompressed version. To accommodate a wider class of compressors that includes the binary quantizer, we further design a novel dynamical scaling mechanism and obtain the linearly convergent Dyna-COLD. Importantly, our results strictly improve existing results for the quantized consensus problem. Numerical experiments demonstrate the advantages of both algorithms under different compressors.
In this paper, the nonlinear U model with time-varying coefficients is investigated and the transformation of the nonlinear model is accomplished by the Newton iterative algorithm. Based on the nonlinear U model, a control algorithm with cerebellar model articulation controller and proportional derivative (PD) in parallel is proposed. The algorithm learns online through a neural network while optimizing the output of the PD, which ultimately enables the actual output of the system to track up to the desired output. Considering that the nonlinear object has the characteristic of rapid change with time, the article improves the PD algorithm to nonlinear PD control algorithm to complete the design of the system. The algorithm automatically adjusts the weights according to the error magnitude to complete the controller parameter adjustment, thus reducing the error of the system. The simulation results show that the nonlinear PD algorithm is better than the PD algorithm, meanwhile, the tracking speed and control precision of the system are improved.
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